A apparatus known as a pneumatic tire vulcanizing apparatus includes upper and lower molds separated from each other upward and downward, each of the molds including multiple sectors separated from one another in a circumferential direction (see Patent Document 1, for example). In such a vulcanizing apparatus, each of the upper mold and the lower mold has a tapered surface formed inclining outward toward mating surfaces of the upper and lower molds; and the sectors slide up and down along the tapered surface, and thus move into a larger diameter and a smaller diameter. In addition, the sectors are always biased by their respective springs to move into the smaller diameter, and are configured to automatically move into the smaller diameter by biasing forces of the respective springs once a vulcanized tire is released from the sectors at the larger diameter. The vulcanizing apparatus provided with these molds has the following problems. First, the vulcanized tire cannot be smoothly released from the sectors in a way that the release of the vulcanized tire is partially delayed, or that protruding portions of the molding surfaces of some of the sectors get stuck in corresponding grooves of the tire. That is because frictional resistance generated when the sectors move into the larger diameter and the smaller diameter is not uniform among the sectors. Second, load on the molds is large. That is because: immediately after the vulcanized tire is released from the sectors, the biasing forces of the springs cause the sectors to move abruptly into the smaller diameter, and thereby to collide with other portions of the mold; or an excessive force is applied to the protruding portions of the molding surfaces of the sectors when the protruding portions get stuck in the grooves of the tire. Patent Document 1: Japanese patent application Kokai publication No. Hei 4-348915